\[x-y^2= xy^2-x^2\]
The right hand side factorises to give
\[x-y^2=x(y^2-x)\]
Subtract
\[x(y^2-x)\]
from both sides to give\[x-y^2+x(x-y^2)=0\]
Now we can factorise both sides completely.
\[(1+x)(x-y^2)=0\]
Hence
\[1+x=0 \rightarrow x=-1\]
and \[y\]
is arbitrary or \[x-y^2=0 \rightarrow y = \pm \sqrt{x}\]
which is the graph of \[y= \sqrt{x}\]
together with it's reflection in the x - axis.